1) The value of ∫1−1(x−[x])dx (where [ . ] denotes greatest integer function) is A) 0 B) 1 C) 2 D) None of these Answer: Option BExplanation:I = ∫1−1(x−[x])dx = ∫1−1xdx−∫1−1[x]dx = [x22]1−1 - [∫0−1[x]dx+∫10[x]dx] = 12[1−1]−[∫0−1[−1]dx+∫100dx] (if -1≤x<0,[x]=-1) (if 0≤x<1, [x] =0) = 0−[−x]1−1−0=0−.[−0−(−1)]=1